Going for two each time Theory

[Buckmulligan]

This should maybe be in the sports section but [censored] it.

The stat for the NFL wide % of successful two point conversions is 50%. Correct me if I'm wrong, but I interpret this to mean that an average offence in the national football league will essentially average an extra point if they went for two each time.

If this is true, what really interests me is this: If you are an NFL coach and you know that your offence is well above the league average, i.e. the colts or the sea hawks, isn't it realistic to assume that you can average more than one point, the reward for an extra point, for each try after a touchdown by going for two and thus rack up something like 7.2-7.5 points per touchdown on average?

There must be some snag here, beacuse this seems to obvious and too good to be true. Any thoughts?

[Mason Hellmuth]

I'm not a huge sports expert, but I think that because an extra point is basically automatic for any team with a reasonably competent kicker, the EV loss of getting no points at all is much larger than the EV gain of getting two.

If the success rate is 50% on two point conversions, obviously your expected value is one point. So assuming 100% extra point attempt success rate and 50% 2 point success rate, the two options have equivalent EV(+1), but much different variance.

Of course 100% is obviously not accurate, and from my brief research i think the 2 point conversion success rate is probably more in the 40-45% range.

The key is recognizing the situations where you want higher or lower variance. Obviously if the game is tied with 1 second left, you'd want to reduce variance and kick it, and if you were down 2 with 1 second left, you'd want to increase your variance. Throughout the game obviously the decision would be less clear cut but would depend on the situation. All things equal though you'd want to choose the play with the higher EV, which in my opinion is kicking the extra point for most if not all teams.

[jstnrgrs]

[ QUOTE ]
If the success rate is 50% on two point conversions, obviously your expected value is one point. So assuming 100% extra point attempt success rate and 50% 2 point success rate, the two options have equivalent EV(+1), but much different variance.

Of course 100% is obviously not accurate, and from my brief research i think the 2 point conversion success rate is probably more in the 40-45% range.

The key is recognizing the situations where you want higher or lower variance. Obviously if the game is tied with 1 second left, you'd want to reduce variance and kick it, and if you were down 2 with 1 second left, you'd want to increase your variance. Throughout the game obviously the decision would be less clear cut but would depend on the situation. All things equal though you'd want to choose the play with the higher EV, which in my opinion is kicking the extra point for most if not all teams.

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The reason that this is not correct is because by going for 2, you are not just risking the 1 point that you could have kicked. You are also risking other points that come into play when the other team adjusts their strategy to the result of your 2 point attempt.

Suppose a team has a 55% chance of making a 2 point conversion. If they run back the opening kickoff for a touchdown, should they go for 2? I think not.

45% of the time, they miss, and the other team can take the lead with a touchdown.

55% of the time, they are sucesful. Of this 50% of the time, the other team can tie with a touchdown (when they go for two because you did).

So 45% of the time, you would trail by a point if the other team scores.

27.5% of the time, you would be tied if the other team scores.

Only 27.5% of the time, you would lead by two points if the other team scores.

Add to this the fact that if you miss, the other team can tie with 2 field goals, and the argument against going for 2 becomes even stronger.

Unless you are playing a game in which scoring is done with basketball frequency, maximizing your expected points is not the same as maximizing your chance to win.

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Unless you are playing a game in which scoring is done with basketball frequency, maximizing your expected points is not the same as maximizing your chance to win.

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I'm assuming most people here read David Sklansky's article a few months back about going for it on 4th down. The basis of his whole article was that you can calculate your EP(expected points) from any field position, your opponents EP from that same spot in case you fail, and your expected 4th down conversion success rate, and then compute your best play from that. He of course offered the caveat that it doesn't apply in certain situations where you'd want to minimize your variance, but in general it is correct. Now i'm not saying this method of analyzing football decisions is correct just because he says it is, but I do think that carries a lot of weight.

That said, I do think there is merit to your point about scoring frequency. Obviously if you scored a touchdown to tie and simultaneously the entire starting offense for the other team tore their ACLs, you'd definitely want to kick, as the chance of them scoring again has suddenly dropped to near 0. But I think that with moderately frequent scoring, maximizing EP is correct under normal circumstances not near the end of the game. But again, I think this will almost always mean kicking the extra point.

[MyTurn2Raise]

[ QUOTE ]
I'm assuming most people here read David Sklansky's article a few months back about going for it on 4th down. The basis of his whole article was that you can calculate your EP(expected points) from any field position, your opponents EP from that same spot in case you fail, and your expected 4th down conversion success rate, and then compute your best play from that. He of course offered the caveat that it doesn't apply in certain situations where you'd want to minimize your variance, but in general it is correct. Now i'm not saying this method of analyzing football decisions is correct just because he says it is, but I do think that carries a lot of weight.


[/ QUOTE ]

I didn't read this, but this idea is pure lunacy

[sam h]

[ QUOTE ]
I'm assuming most people here read David Sklansky's article a few months back about going for it on 4th down. The basis of his whole article was that you can calculate your EP(expected points) from any field position, your opponents EP from that same spot in case you fail, and your expected 4th down conversion success rate, and then compute your best play from that. He of course offered the caveat that it doesn't apply in certain situations where you'd want to minimize your variance, but in general it is correct. Now i'm not saying this method of analyzing football decisions is correct just because he says it is, but I do think that carries a lot of weight.

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Did David pass this off as his own idea? Because a statistics professor at Berkeley wrote a paper a few years back that got a fair amount of press which basically argued the same thing and found that teams should go for it around midfield in 4th and short situations almost every time.

[kenberman]

if you get 2 points half the time, and 0 the other half, isn't that the same thing as getting 1 all the time?

also, that 50% stat may be skewed towards teams who already attempt more than 2 points conversions than the average team b/c they are better talented.

but I dunno. the sample size is prolly to small to know for sure. nobody wants to score a TD, miss a 2 pt conversion, then have the other team take the lead w/ a TD and kick

[trying2learn]

as soon as you drop the stat to 49% it makes sense why they wouldn't try that. you're further from a lock that you'll make two half the time, than you are from a lock that you'll make one 100% of the time.

[Triumph36]

No - it would just be increasing variance needlessly. Plus, the teams you'd score 2 on more often are probably teams you should be beating, and the teams you'd miss against are teams you need every point against.

Teams are not going to start going for 2 regularly.